A Partitioned Finite Difference Method for Heat Transfer with Moving Line and Plane Heat Sources

Area of Science:

• Thermodynamics
• Computational Physics
• Numerical Analysis

Background:

• Irreversible thermodynamic processes often involve heat transfer with moving singular sources.
• Accurate simulation of these processes requires handling solution singularities near heat sources.
• Local entropy production analysis is critical for understanding energy distribution in non-equilibrium systems.

Purpose of the Study:

• To develop an efficient numerical scheme for simulating heat transfer governed by the diffusion equation with moving singular sources.
• To accurately resolve solution singularities near heat sources for precise local entropy production analysis.
• To provide a reliable tool for large-scale simulations of dissipative systems.

Main Methods:

• A finite difference framework with a partitioned discretization strategy was employed.
• Analytical derivation and incorporation of solution "jump" conditions near the source.
• Hybrid approach combining specialized approximations near the source and standard schemes away from it.

Main Results:

• The proposed method achieves globally second-order convergent spatial discretization.
• A sparse system is generated, enabling efficient large-scale simulations.
• Numerical examples demonstrate the accuracy and efficacy of the developed scheme.

Conclusions:

• The developed numerical scheme is efficient and accurate for simulating heat transfer with moving singular sources.
• The method provides a reliable tool for studying energy distribution in non-equilibrium thermal processes.
• This work contributes to the understanding of complex thermodynamic systems.